Benn tied it 3-3 on the power play at 16:19, putting a rebound past Talbot.
Lindell scored on the power play at 10:25 of the third period to give the Stars a 4-3 lead.
"It's disappointing when you have a lead late in the third, you have to find a way to hunker down and get the job done," Bishop said. "They didn't give up and found a way to get some goals late."
Nugent-Hopkins tied it 4-4 at 12:16 on a shot from the slot that hit Stars defenseman Dan Hamhuis and went past Bishop.
"We know that [scoring], we have that in our room, we're capable of that," Nugent-Hopkins said. "We went through a stretch like this last year where it was kind of the same thing, we were putting a lot on net but just weren't able to score on second and third opportunities. Tonight it kind of clicked for us, so we want to keep that rhythm and get on a roll here."
Edmonton ended a three-game home losing streak.
"That's the big hump we got over as a team," Oilers coach Todd McLellan said. "I could talk about the negatives that we have to fix, but I'm going to focus on us having the ability to outscore that team 5-1 at even strength. That's a good sign."